Modeling and Analysis of Wireless Channels via the Mixture of Gaussian Distribution

Abstract

In this paper, we consider a unified approach to model wireless channels by the mixture of Gaussian (MoG) distribution. The proposed approach provides an accurate approximation for the envelope and the signal-to-noise ratio (SNR) distributions of wireless fading channels. Simulation results have shown that the proposed model can accurately characterize multipath and composite fading channels. We utilize the well-known expectation-maximization (EM) algorithm to estimate the parameters of the MoG distribution and further utilize the Bayesian information criterion (BIC) to determine the number of mixture components automatically. We employ the Kullback-Leibler (KL) divergence and the mean-square-error (MSE) criteria to demonstrate that the proposed distribution provides both high accuracy and low computational complexity. Additionally, we provide closed-form expressions or approximations for several performance metrics used in wireless communication systems, including the moment generating function (MGF), the raw moments, the amount of fading (AF), the outage probability, the average channel capacity, and the probability of energy detection for cognitive radio (CR). Numerical analysis and Monte Carlo simulation results are presented to corroborate the analytical results.